In the recent past, some researchers studied some fixed point results on the modular variable exponent sequence space , where and . They depended on their proof that the modular has the Fatou property. But we have explained that this result is incorrect. Hence, in this paper, the concept of the premodular, which generalizes the modular, on the Nakano sequence space such as its variable exponent in and the operator ideal constructed by this sequence space and -numbers is introduced. We construct the existence of a fixed point of Kannan contraction mapping and Kannan nonexpansive mapping acting on this space. It is interesting that several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of summable equations are introduced. The novelty lies in the fact that our main results have improved some well-known theorems before, which concerned the variable exponent in the aforementioned space.

中文翻译：

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中野序列空间上 Kannan 映射的一些不动点结果

近年来，一些研究人员研究了模变指数序列空间上的一些不动点结果，其中 和 . 他们依赖于证明模块具有 Fatou 属性的证据。但是我们已经说明这个结果是不正确的。因此，在本文中，在中野序列空间上推广模的预模的概念，例如其变量指数在并引入了由该序列空间和-数构造的算子ideal 。我们构造了作用于该空间的 Kannan 收缩映射和 Kannan 非膨胀映射的不动点的存在性。有趣的是，提出了几个数值实验来说明我们的结果。此外，还介绍了可加方程解存在性的一些成功应用。新颖之处在于，我们的主要结果改进了之前一些众所周知的定理，这些定理涉及上述空间中的变量指数。